Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C11×#423 ⋊ C2 |
| Sylow | C11 ⋊ #2932 |
484 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 181 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 704 |
Polycyclic presentation:
2^7,11|a^2=f,c^2=f,f^2=g,b^a=be,c^a=cg,d^a=dg,d^b=dg,h^b=h^10,h^c=h^10184 conjugacy classes — view the full character table.
| maximal subgroup of | #14647902, #14647906, #14647916, … |
| maximal normal subgroup of | #14647902, #14647906, #14647916, … |
| maximal quotient of | #14724480, #14724487, #14724495, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 13227);